Abstract
The full discretization of the semilinear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is used for the temporal approximation. We study the stability under a CFL condition and prove optimal strong convergence rates of the fully discrete scheme. Numerical experiments illustrate our theoretical results. Further, we analyze and bound the expected energy and numerically show excellent agreement with the energy of the exact solution.
| Original language | English |
|---|---|
| Pages (from-to) | 1976–2003 |
| Number of pages | 28 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 59 |
| Issue number | 4 |
| Early online date | 15 Jul 2021 |
| DOIs | |
| Publication status | Published - 2021 |
Keywords
- Discontinuous Galerkin finite element method
- Energy conservation
- Semilinear stochastic wave equation
- Stability
- Stochastic Verlet integration
- Strong convergence
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
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© 2021, Society for Industrial and Applied Mathematics Read More: https://epubs.siam.org/doi/10.1137/20M1364746